Numbers such that Tau divides Phi divides Sigma/Examples/3

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Examples of Numbers such that Tau divides Phi divides Sigma

The number $3$ has the property that:

$\map \tau 3 \divides \map \phi 3 \divides \map \sigma 3$

where:

$\backslash$ denotes divisibility
$\tau$ denotes the $\tau$ (tau) function
$\phi$ denotes the Euler $\phi$ (phi) function
$\sigma$ denotes the $\sigma$ (sigma) function.


Proof

\(\ds \map \tau 3\) \(=\) \(\, \ds 2 \, \) \(\ds \) $\tau$ of $3$
\(\ds \map \phi 3\) \(=\) \(\, \ds 2 \, \) \(\ds \) $\phi$ of $3$
\(\ds \map \sigma 3\) \(=\) \(\, \ds 4 \, \) \(\, \ds = \, \) \(\ds 2 \times 2\) $\sigma$ of $3$

$\blacksquare$